Question

Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to △ABC with its sides equal to \((\frac{5}4)^{th}\) of the corresponding sides of △ABC.

Answer 1

The steps involved in the required construction are: 

(1) Draw a line segment AB = 4.5 cm.

(2) Using a protractor, draw ∠BAD=90°. Taking A as the center and radius 4.5 cm, draw an arc, intersecting AD at C. Join BC.

(3) Draw any line segment AE, making an acute angle with AB and opposite to the vertex C. Taking A as the center and any radius, draw an arc, intersecting AE at F. Taking F as the center and radius AF, draw an arc, intersecting AE at G. Similarly, repeat the process 3 more times to get points H, I and J. Join BI.

(4) Taking I as the center and any radius, draw an arc., intersecting AE and BI at K and L respectively. Taking J as the center and radius IK, draw an arc., intersecting AE at M. Taking M as the center and radius KL, draw an arc, intersecting previous arc at N. Join and extend JN, intersecting extended AB at O.

(5) Taking B as the center and any radius, draw an arc., intersecting BA and BC at Q and R respectively. Taking O as the center and radius BQ, draw an arc., intersecting AO at S. Taking S as the center and radius QR, draw an arc, intersecting previous arc at T. Join and extend OT, intersecting AD at P.

(6) ∆AOP is the required triangle.